Hi there - All shimano spd cleats will fit the spin bikes. I faced a similar problem when I started spin classes. I ride Eggbeaters on both my mountain and road bikes - so my cleats wouldn't work in class.
Spin bikes usually take traditional spds or there are a few in my class that are set up for Look type pedals.
What I ended up doing was just finding a new pair of shoes on sale and getting spds - so now I have a pair of shoes just for spin class. It actually works out well because they just live in my gym bag and aren't nearly as trashed as the ones I wear mountain biking.
Have fun spinning - I'm a junky these days - doing a two hour class tonight.
Problems are like goldfish ~ The more you feed them the bigger they get!
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